-16 dx 1. X=2 sec(e) 2. x= 2sin(e) 4-X dx 3. X= 4tan(e) 4. X= 4sec(e) SV16+ x² dx x²-4 dx

Q: ind the general solution to the differential equation. dx dt = 3t2(x2 + 25) x =

A: topic- differential equations

Q: Solve the differential equation by variation of parameters. y" + y = sin?(x) sinx ( sin’'x cos (x) +…

A: Solve the above questions

Q: Solve the equation difFerential Ci+ x) y' + y = Jx %3D

A: Given differential equation is,

Q: Solve differential equation  [Sin(xy)+xycos(xy)+2x]dx = [x^2cosxy+2y]dy

A: GIVEN : (sin(x,y)+x y cos(x,y)+2x)dx+(x2cos(x y)+2y)dy=0 let P(x,y)=sin(x,y)+x y cos(x,y)+2x  and…

Q: 1. S(7x³ + 4x²)dx e*dx 2. J itez* 1+e2x 3. S(V1 – cos x)dx

A: We will these indefinite integrals as

Q: 30. 5e dx 31. dx Зи du - 1 33. 3. x² dx 35. (x' + 5)* 37. ((3 In z + 2)4 39 dz

A: We have to solve the integration

Q: dly dx2 - 2 dy dx -3y = COS X

A: The given differential equation is d2ydx2-2dydx-3y=cosx. We have to find the solution of the given…

Q: d) sin(x)y' + cos(x)y = tan(x)

A: We have to solve

Q: arctan x Xe fel Xaresecx d

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: 7. f (ex + 1)² dx 8. fex dx/(e²x + 3) 9. f (cos x-sin x)² dx

A:

Q: A company will sell N units of a product after spending $x thousand in advertising, as given by N =…

A: We are given that N=50x-x2, 5≤x≤25. Now, dN=50-2x dx. First, increase the advertising budget from…

Q: tan20 sec2ede In 2 edx 3. 1. (a² + a²tan²0)² 2ex- 1 x'dx dx x- 1 2. 4. (1+ x2)3

A: As per our policy, only the first three subdivisions will be solved. For the remaining subdivision,…

Q: Ssin(2x+3)dx= d -1 cos(2.x+ 3)+C 2 a 5 cos(2.x + 3)+C -1 cos(2x+3)+C - cos(2x+3)+ C e cos(2x +3)+ C

A:

Q: 6. sin'x dx 7. cos*x dx 4x+ 2 dx x +x + 5 8. .2 (1+x*)dx 2x-1 dx 2-8x + 15 10. 2x+x +1 1. dx (x-1)…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: Solve differential equetion. = 8X+_5X dx 4-202

A:

Q: 10. (2х + Зу — 5)dx + (3х — у — 2)dy %3D 0 hint: Ca

A: We are asked to solve the differential equation.

Q: Find dy/dx by implicit differentiation. xy + 2x + 2x2 = 3

A: Given, xy + 2x + 2x2 = 3

Q: e2x dx 1. Зе2x+1 2. sinx dx 1 3. cos 2x

A: As per bartleby guidelines we are supported to answer only first three subparts,  kindly repost…

Q: 10. Find the derivative of y = ln 4**+1) In 4 dy A) dx 2x dy 2x In 4 B) dx dy 2xIn 4 C) dx 4(*+1) dy…

A:

Q: 2. Cosh X y sinh x 2 cosh x sin dx dy dxxy = 1 5. (1-x)

A:

Q: Evaluate (indefinite integral) (4x^2.5 - x^e - 2sinx)dx (t^3 + 5t^2 - 4)/ (t^2) dt

A:

Q: Calculate dy/dx. You need not expand your answer. y =x2.3/9+2/x2.3)(9x − 1) Answer ----->dy/dx:…

A:

Q: | (3x – 2x + 1) dx 5. |(x - 1)° dx 6. 7. (x² – x*) dx 8. cos x dx /2 I sec' x dx 9. dx 11. (4 – 2x')…

A: 5. I=∫13(3x2-2x+1)dx =∫133x2dx-∫132xdx+∫13dx =3∫13x2dx-2∫13xdx+∫13dx =3x3313-2x2213+x13…

Q: 30. 5e dx 31. Зи du - 1 33. x² dx 35. (x+5)* 37. xp (3 In z + 2)4 39, -dz

A: We will solve the integration.

Q: The integrating factor of the linear differential equation – (tanx)y = x is_ - O sinx O log(cosa)…

A: Given dydx-tanxy=x

Q: 7. Differentiate the following function.   y=ln(x+6)+ln5 dy/dx=nothing   Enter your answer in the…

A: Differentiate the following function.      y=ln(x+6)+ln5

Q: 8. dx +x2 Integrate:

A:

Q: 5. dx of y = (1+e-*)²/(1-e-*)

A: We need to find the derivative of the given function.

Q: Differentiate the following function.   y=ln(x+1)+ln7 dy/dx=?

A:

Q: Integrate dx/(x+1)(x^2+16) from 0 to 1

A:

Q: 6) S sech? (2x- 3) dx | ex-e-x 7) S ex+e-x 8) S(eax – e-ax) dx sinh x 9) S dx 1+cosh x 10) ſ csch? x…

A: Given

Q: valuate f¹² Vsin x + 1 cos x dx.

A: Topic:- application of integration

Q: 8) S(eax - e-ax) dx 9) S; sinh x dx 1+cosh x

A: Answer to question number 8 and 9 are as below,

Q: Vsin x.cos x 1+ 2.ln x 3y (аns.: 4

A: Given                   y43= sinx cosx1+2.lnx

Q: 6) S sech (2x - 3) dx 7)S e-e-x e*te-x dx 8) [(eax – e-ax) dx sinh x 9) S 1+coshx dx

A:

Q: A population x of rats satisfies the DE dx /dt ka?. Initially there are x(0) = 2 rats, and their…

A: The general solution of a differential equation always contains a constant of integration. The…

Q: S(2x% + 3x -1)dx - 3x –1 dx Integrate

A:

Q: sin 6x dx sin23x 4. 6. S Ve3x + e 4x dx ex dx 8. J 1+ e2x

A:

Q: Uniclaretiana Fundoción universitaria Claretiana 1 (In x - 4) dx – (x + 1) dy = 0 2 4 +6x) dx +…

A:

Q: 9. S sec 2x dx 10. S cos x esin x dx 11. dx x+1

A: Evaluation of the above integration is

Q: 3e° 3ecsch 3x 11) -dx sinh 3x tanh 3x

A:

Q: 1. S(e2x – 1)3 dx 3. S sin 2x (sin®x + 1) dx 2. S(x6 – 3x²)ª (x5 – x) dx -

A:

Q: 6. A certain radioactive material has a half-life of 100 days. If the amount of material present, x,…

A:

Q: 4) [ sinh 2xdx 5) [ e* sin e"dx 6) fcosh'vdv

A: Given:  4) ∫0π2 sinh(2x)dx5) ∫ln(π)2exsinexdx6) ∫cosh2vdv

Q: 1. S(esin *cos x – acos 2x sin 2x)dx 2. S(etan x sec x- esecx tanx)sec x dx 3. S dx xvax - 16 3x-2…

A:

Q: dy 1- Find by implicit differentiation. 2- x2 + y2 = 100. 3- x³ + y³ = 3xy². 4- x²y + 3xy³ – x = 3.…

A:

Q: 12. Differentiate.   y=4/2−7x dy/dx=nothing   Enter your answer in the answer box.

A:

Q: Find dy/dx by implicit differentiation. 3x2 + 5xy - y2 = 4 dy/dx =

A: Given; 3x^2+5xy-y^2=4 dy/dx=?

Q: (1) S(1+ x² ) (2 - x) dx (2) S V? + 4 dx 3) § *³ +2x². dx x* (4) S" 5 e* + 3 sinx dx

A: Note to student : Thanks for posting your queries. But the photo contain multiple questions. As per…

Q: 2 1) (-2xy) dx + (Siny-x²) dy

A: see my solutions

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.